POLARIZATION-INVERTED HIGHER-ORDER PLATE-MODE RESONATORS AND METHODS FOR MAKING THE SAME
Disclosed are polarization-inverted higher-order plate-mode resonators and methods for making the same. In an aspect, a plate-mode resonator includes a first piezoelectric layer having a first crystal orientation specified by a first set of Euler angles α 1 , β 1 , and γ 1 , a dielectric layer disposed on a top surface of the first piezoelectric layer, a second piezoelectric layer, disposed on a top surface of the dielectric layer, having a second crystal orientation specified by a second set of Euler angles α 2 , β 2 , and γ 2 , wherein az is approximately equal to α 1 , wherein a difference between β 2 and β 1 is approximately 180 degrees, and wherein γ 2 is approximately equal to γ 1 , and a metallization structure disposed on a top surface of the second piezoelectric layer, the metallization structure comprising at least one interdigital transducer.
1 . A plate-mode resonator, comprising:
a first piezoelectric layer having a first crystal orientation specified by a first set of Euler angles α 1 , β 1 , and γ 1 ;
a dielectric layer disposed on a top surface of the first piezoelectric layer;
a second piezoelectric layer, disposed on a top surface of the dielectric layer, having a second crystal orientation specified by a second set of Euler angles α 2 , β 2 , and γ 2 , wherein α 2 is approximately equal to α 1 , wherein a difference between β 2 and β 1 is approximately 180 degrees, and wherein γ 2 is approximately equal to γ 1 ; and
a metallization structure disposed on a top surface of the second piezoelectric layer, the metallization structure comprising at least one interdigital transducer.
2 . The plate-mode resonator of claim 1 , wherein the first piezoelectric layer, the dielectric layer, and the second piezoelectric layer resonate in a symmetric plate mode.
3 . The plate-mode resonator of claim 1 , wherein the first piezoelectric layer comprises a z-cut crystal and wherein the second piezoelectric layer comprises an inverted z-cut crystal.
4 . The plate-mode resonator of claim 1 , wherein the first piezoelectric layer has the Euler angle β 1 =−180, and wherein the second piezoelectric layer has the Euler angle β 2 =0.
5 . The plate-mode resonator of claim 1 , wherein the first piezoelectric layer has the Euler angle β 1 =−148, and wherein the second piezoelectric layer has the Euler angle β 2 =32.
6 . The plate-mode resonator of claim 1 , wherein the first piezoelectric layer has the Euler angle γ 1 =0, and wherein the second piezoelectric layer has the Euler angle γ 2 =0.
7 . The plate-mode resonator of claim 1 , wherein the first piezoelectric layer has the Euler angle α 1 =90, and wherein the second piezoelectric layer has the Euler angle β 2 =90.
8 . The plate-mode resonator of claim 1 , wherein the first piezoelectric layer has the Euler angles α 1 =90, β 1 =−180, and γ 1 =0, and wherein the second piezoelectric layer has the Euler angles α 2 =90, β 2 =0, and γ 2 =0.
9 . The plate-mode resonator of claim 1 , wherein the first piezoelectric layer has the Euler angles α 1 =90, β 1 =−148, and γ 1 =0, and wherein the second piezoelectric layer has the Euler angles α 2 =90, β 2 =32, and γ 2 =0.
10 . The plate-mode resonator of claim 1 , wherein the dielectric layer comprises silicon dioxide (SiO 2 ), carbon-doped silicon dioxide, fluorine-doped silicon dioxide, silicon nitride (Si 3 N 4 ), carbon-doped silicon nitride, fluorine-doped silicon nitride, or a combination thereof.
11 . The plate-mode resonator of claim 1 , wherein at least one of the first piezoelectric layer and the second piezoelectric layer comprises lithium niobate (LiNbO 3 ), lithium tantalate (LiTaO 3 ), or a combination thereof.
12 . The plate-mode resonator of claim 1 , wherein the first piezoelectric layer, the dielectric layer, and the second piezoelectric layer suspend over a cavity.
13 . A method for fabricating a plate-mode resonator, the method comprising:
providing, on a substrate, a first piezoelectric layer having a first crystal orientation specified by a first set of Euler angles α 1 , β 1 , and γ 1 ;
forming a dielectric layer on a top surface of the first piezoelectric layer;
providing a second piezoelectric layer on a top surface of the dielectric layer, the second piezoelectric layer having a second crystal orientation specified by a second set of Euler angles α 2 , β 2 , and γ 2 , wherein α 2 is approximately equal to α 1 , wherein a difference between β 2 and β 1 is approximately 180 degrees, and wherein γ 2 is approximately equal to γ 1 ; and
forming a metallization structure on a top surface of the second piezoelectric layer, the metallization structure comprising at least one interdigital transducer.
14 . The method of claim 13 , wherein providing the first piezoelectric layer comprises providing the first piezoelectric layer as a z-cut crystal and wherein providing the second piezoelectric layer comprises providing the second piezoelectric layer as an inverted z-cut crystal.
15 . The method of claim 13 , wherein providing the first piezoelectric layer comprises providing the first piezoelectric layer having the Euler angle β 1 =−180, and wherein providing the second piezoelectric layer comprises providing the second piezoelectric layer having the Euler angle β 2 =0.
16 . The method of claim 13 , wherein providing the first piezoelectric layer comprises providing the first piezoelectric layer having the Euler angle β 1 =−148, and wherein providing the second piezoelectric layer comprises providing the second piezoelectric layer having the Euler angle β 2 =32.
17 . The method of claim 13 , wherein providing the first piezoelectric layer comprises providing the first piezoelectric layer having the Euler angle γ 1 =0, and wherein providing the second piezoelectric layer comprises providing the second piezoelectric layer having the Euler angle γ 2 =0.
18 . The method of claim 13 , wherein providing the first piezoelectric layer comprises providing the first piezoelectric layer having the Euler angle α 1 =90, and wherein providing the second piezoelectric layer comprises providing the second piezoelectric layer having the Euler angle α 2 =90.
19 . The method of claim 13 , wherein providing the first piezoelectric layer comprises providing the first piezoelectric layer having the Euler angles α 1 =90, β 1 =−180, and γ 1 =0, and wherein providing the second piezoelectric layer comprises providing the second piezoelectric layer having the Euler angles α 2 =90, β 2 =0, and γ 2 =0.
20 . The method of claim 13 , wherein providing the first piezoelectric layer comprises providing the first piezoelectric layer having the Euler angles α 1 =90, β 1 =−148, and γ 1 =0, and wherein providing the second piezoelectric layer comprises providing the second piezoelectric layer having the Euler angles α 2 =90, β 2 =32, and γ 2 =0.
21 . The method of claim 13 , wherein the dielectric layer comprises silicon dioxide (SiO 2 ), carbon-doped silicon dioxide, fluorine-doped silicon dioxide, silicon nitride (Si 3 N 4 ), carbon-doped silicon nitride, fluorine-doped silicon nitride, or a combination thereof.
22 . The method of claim 13 , wherein at least one of the first piezoelectric layer and the second piezoelectric layer comprises lithium niobate (LiNbO 3 ), lithium tantalate (LiTaO 3 ), or a combination thereof.
23 . The method of claim 13 , further comprising removing the substrate below a portion of the first piezoelectric layer.